The proposed 3GPP’s 5G Next-generation (NextGen) Core architecture (5GC) enables the ability to introduce new user and control plane functions within the context of network slicing to allow greater flexibility in handling of heterogeneous devices and applications. In this paper, we discuss the integration of such architecture with future networking technologies by focusing on the information ce...

For k = 0, 1, 2, 3, 4, 5, let Pk be the class of k-edge-connected 5regular planar graphs. In this paper, graph operations are introduced that generate all graphs in each Pk. ∗Research partially supported by NSF grants DMS-0556091 and ITR-0326387. †Research partially supported by Board of Regents grant LEQSF(2004-07)-RD-A-22.

By applying the Tutte decomposition of 2{connected graphs into 3{block trees we provide unique structural characterizations of several classes of 2{connected graphs, including minimally 2{connected graphs, minimally 2{edge{connected graphs, critically 2{connected graphs, critically 2{edge{connected graphs, 3{edge{connected graphs, 2{connected cubic graphs and 3{connected cubic graphs. We also g...

We propose a simple and natural definition for the Laplacian and the signless Laplacian tensors of a uniform hypergraph. We study their H-eigenvalues, i.e., H-eigenvalues with nonnegative H-eigenvectors, and H-eigenvalues, i.e., H-eigenvalues with positive H-eigenvectors. We show that each of the Laplacian tensor, the signless Laplacian tensor, and the adjacency tensor has at most one H-eigenva...

Let l > 0 and k ≥ 0 be two integers. Denote by C(l, k) the family of 2-edge-connected graphs such that a graph G ∈ C(l, k) if and only if for every bond S ⊂ E(G) with |S| ≤ 3, each component of G − S has order at least (|V (G)| − k)/l. In this paper we prove that if a 3-edge-connected graph G ∈ C(12, 1), then G is supereulerian if and only if G cannot be contracted to the Petersen graph. Our re...

Let G be a 2-edge-connected undirected graph, A be an (additive) Abelian group, and A = A − {0}. A graph G is A-connected if G has an orientation D(G) such that for every mapping b: V (G) → A satisfying  v∈V (G) b(v) = 0, there is a function f : E(G) → A ∗ such that for each vertex v ∈ V (G), the sum of f over the edges directed out from v minus the sum of f over the edges directed into v eq...

The super connectivity κ ′ and the super edge-connectivity λ′ are more refined network reliability indices than connectivity κ and edge-connectivity λ. This paper shows that for a connected graph G with order at least four rather than a star and its line graph L(G), κ ′(L(G))= λ′(G) if and only if G is not super-λ′. As a consequence, we obtain the result of Hellwig et al. [Note on the connectiv...

We show that if a graph is k-edge-connected, and we adjoin to it another graph satisfying a " contracted diameter ≤ 2 " condition, with minimal degree ≥ k, and some natural hypothesis on the edges connecting one graph to the other, the resulting graph is also k-edge-connected.

In 1978, Chvátal and Thomassen proved that every 2-edge-connected graph with diameter 2 has an orientation with diameter at most 6. They also gave general bounds on the smallest value f(d) such that every 2-edge-connected graph G with diameter d has an orientation with diameter at most f(d). For d = 3, their general bounds reduce to 8 ≤ f(3) ≤ 24. We improve these bounds to 9 ≤ f(3) ≤ 11.

In this note we provide a generalization of a result of Goddard, Raines and Slater [4] on edge-connectivity of permutation graphs for hypergraphs. A permutation hypergraph Gπ is obtained from a hypergraph G by taking two disjoint copies of G and by adding a perfect matching between them. The main tool in the proof of the graph result was the theorem on partition constrained splitting off preser...